外文文獻(xiàn)翻譯--一種關(guān)于平臺(tái)型機(jī)械臂正運(yùn)動(dòng)學(xué)問(wèn)題完整通用的解決方法（英文）

1、A Complete and General Solution to the Forward Kinematics Problem of Platform-Type Robotic Manipulators Xiaolun Shi Department of Systems Engineering The Chinese University of Hong Kong Abstract In this paper a genera

2、l method is presented, based on the data of three point positions, velocities and ac- celerations of the end effector, for solving the forward kinematics problem of any platform- type manipulator, including the 6 DO

3、F Stewart Platform. Numerical ex- amples are included to demonstrate the application of the method. It is shown that the equations for the for- ward position kinematics are highly-nonlinear, how- ever, closed-form so

4、lutions to the forward rate kine- matics and the forward acceleration kinematics can be obtained by solving a system of linear equations. The advantages of using additional passive joint en- coders is also discussed,

5、 to simplify the solution of the position kinematics problem, and obtain a one-to-one relation between the actuated joint variables and the end effector configurations. 1 Introduction The anthropomorphic open chain me

6、chanisms of serial type industrial robot arms have a number of advan- tages such as long reach, large workspace and dextrous maneuverability. However, the low rigidity of the can- tilevered structure of the open cha

7、in mechanism is a serious disadvantage, and it is not suitable for high speed or precision operations. An alternative to the serial type manipulation de- vice is the parallel mechanism such as the Stewart Platform [

8、l]. The reduced mass of the moving parts, toget her with the significantly improved endpoint stiff- ness of the truss-like structure of the parallel mecha- nism, results in high positioning accuracy and good dynami

9、c performance. A great deal of research work has been done in the area of the kinematic analysis of parallel manipulators. Hunt [2], in his book, suggested that the manipula- tion capability of the parallel mechanism

10、 be utilized in robots and he later [3] listed a number of possible structures of parallel mechanisms suitable for robotic applications. Yang et. al. [4], from the kinematic point of view, studied the feasibility of

11、applying such a mechanical device in robotics. Fitcher [5] performed a detailed theoretical and experimental investigation of R.G. Fenton Department of Mechanical Engineering The University of Toronto a Stewart Platf

12、orm type manipulator. Recently, Mo- hamed et. al. [6], Sugimoto [7], Shi et al. [8] and Behi [9] respectively, developed computational schemes for solving the instantaneous kinematics of parallel mech- anisms, such a

13、s the Stewart Platform, using screw the- ory, the concept of Partial Twist [6] and other tech- niques. Lee et al. [lo] and Waldron et al. [ll], re- spectively, developed solutions to the forward position kinematics

14、 problem for a 3 DOF in-parallel-actuated manipulator, and a hybrid serial-parallel manipulator containing a 3 DOF parallel module. Nanua et al. [12] presented a solution for the forward position kinemat- ics of a sp

15、ecial form of the 6 DOF Stewart Platform. However, most of these methods either involve all passive joint variables and thus the solution proce- dures are very complicated, or can only be applied to certain simplified

16、 versions of the platform-type ma- nipulator. An effective, general and unified solution for the forward kinematics problem of platform-type manipulators, including position, velocity and acceler- ation kinematics, i

17、s still unavailable at present. In this paper, a general method is presented for solv- ing the forward kinematics problem of platform-type manipulators, using the positions, velocities, and ac- celerations of three po

18、ints of the moving platform (end effector). This method requires the solution of only a few of the passive joint variables and thus the method is computationally efficient, and its implementation is straightforward.

19、2 Forward Position Kinematics Let us first consider a 6 DOF Stewart Platform as shown in Figure 1. The three non-collinear points of the moving platform under consideration are, re- spectively, pi (i = 1,3). The coord

20、inates of the three points expressed with respect to the base reference frame (0 - X - Y - 2) can be represented by 1050-4729B4 $03.00 0 1994 IEEE 3055 Figure 3: The top view of a symmetric 6 DOF plat- form S

21、imilarly, the unit vector j representing the orien- tation of the ,ye axis with respect to the base frame is The unit vector k representing the orientation of the ze axis with respect to the base, then, can be deter-

22、 mined using the cross product 2 4k = i x j = ?= q; sin sin(a; + 7i) L?,) = q; sin P ;cos(ai + 7;) [RI and P, in general, contain six unknown vari- ables, a; and Pi, which must be eliminated before the positi

23、on and orientation of the end effector can actu- ally be determined. To this end, six constraint equa- tions are required, of which three can be obtained us- ing the three point vectors, pi, points are the centers of